(22) Y (F2 x2) Suppose x 3 -F is a repeated factor of X3, then y 3 = G, and X 3 = (x 3 -F)2 [P' _ P(X3+F)2+2' _ G(X +F) -G 2 ], (23) nd putting x3-F=y, (y) 2= 7'3'2- [41' r 1' F 2 -{-4 g r qFG - G2 +2 (2P'r 19F+9 r q G) y+ r y (24) o that the stability of this axial movement is secured if A = 4 P' r ?'F 2 + 4 Y q FG - G 2 (25) s negative, and then the axis makes r J l (-A)/7r nutations per second.